Transformations and invariants for dihedral Gauss hypergeometric functions
Classical Analysis and ODEs
2013-10-04 v1
Abstract
Hypergeometric equations with a dihedral monodromy group can be solved in terms of elementary functions. This paper gives explicit general expressions for quadratic monodromy invariants for these hypergeometric equations, using a generalization of Clausen's formula and terminating double hypergeometric sums. Besides, pull-back transformations for the dihedral hypergeometric equations are presented, including Klein's pullback transformations for the equations with a finite (dihedral) monodromy group.
Cite
@article{arxiv.1101.3688,
title = {Transformations and invariants for dihedral Gauss hypergeometric functions},
author = {Raimundas Vidunas},
journal= {arXiv preprint arXiv:1101.3688},
year = {2013}
}
Comments
29 pages; a split off from arxiv.org/0807.4888